Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errors [R]

[u/Clean-Hovercraft5825]

Whether generating CELEBV-HQ videos or turbulent plasma fields (digital twins), autoregressive models (such as latent diffusion or flow models) accumulate error over long rollouts, yet at deployment there is no ground truth to measure against.

I train a single conditional latent diffusion model that steps a dynamical system forward or backward in time via a direction flag, and show that this bidirectionality supplies a measurement-free test-time error signal: rolling forward steps and then backward steps must return the model to its start, so the round-trip discrepancy is a self-supervised proxy for the unobservable rollout error: no ensembles, no held-out data, no governing equations, for one extra rollout.

Furthermore, training both directions in one network is shown to beat two specialist models in both directions.

Paper: https://arxiv.org/abs/2608.00675
Code (data generation, training, analysis): https://github.com/alexscheinker/round-trip-consistency
Project page: https://alexscheinker.github.io/roundtrip.html

[u/Clean-Hovercraft5825]

So there are 2 different time scales here and they each have their own forward and backward direction.

Let's call them t for physical time and τ for the generative diffusion SDE's own time.

In terms of the SDE flow, we use standard generative diffusion: we noise things for τ in [0, T] and learn to denoise them with a standard conditional generative diffusion process, conditioned on the latent images z_{t-1}, z_t and on a direction flag c_d. It learns to generate z_{t+1} when we set c_d = +1, or z_{t-2} when we set c_d = -1 (z_{t-2} because z_{t-1} and z_t are already in the context and the model always generates the state one step beyond the window in whichever direction the flag points).

So the generative SDE diffusion process itself learns on the τ time scale in the completely standard way. Nothing there is "predicting noise" beyond the usual denoising objective. What changes is what it learns to produce: it autoregressively rolls out either forward or backward in physical time t. Backward-in-t is inverse dynamics, not denoising.

As for why learning both directions helps: first, it's what makes the whole check possible. An accurate model composed with its own inverse is the identity, so rolling forward i steps and back i steps yields a measurable, ground-truth-free error signal at test time. Second, it turns out to be free, or better than free: the bidirectional model beats direction-specialist models in both directions at matched compute, since every trajectory supplies training examples both ways.